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What's FOIL?

Definition: FOIL

Summary

  1. FOIL is an acronym that tells us the steps we need to multiply two binomials
  2. a+b and c+d are binomials
  3. Multiply the first terms, ac
  4. Multiply the outer terms, ad
  5. Multiply the inner terms, bc
  6. Multiply the last terms, bd
  7. 4x+2 and 2x-3 are binomials
  8. 4x•2x are the first terms
  9. 4x•-3 are the outer terms
  10. 2•2x are the inner terms
  11. 2•-3 are the last terms
  12. Multiply out each term to simplify
  13. -12x+4x=-8x

Notes

    1. A binomial is a polynomial with two terms
    1. First we multiply the first terms of each binomial together
    2. Then we multiply the first term of the first binomial by the second term of the second binomial
    3. Then we multiply the second term of the first binomial by the first term of the second binomial
    4. Finally we multiply the second terms of each binomial together
    1. a+b and c+b are binomials, because they each have two terms
    1. Our FIRST terms are 'a' and 'c'
    2. Multiply 'a' and 'c' together to get 'ac'
    1. Our OUTER terms are 'a' and 'd'
    2. Multiply 'a' and 'c' together to get 'ad'
    1. Our INNER terms are 'b' and 'c'
    2. Multiply 'b' and 'c' together to get 'bc'
    1. Our LAST terms are 'b' and 'd'
    2. Multiply 'b' and 'd' together to get 'bd'
    1. 4x+2 and 2x-3 are binomials, because they each have two terms
    1. The first terms are 4x and 2x
    2. This gives us the first term in our polynomial
    1. The outer terms are 4x and -3
    2. This gives us the second term in our polynomial
    1. The inner terms are 2 and 2x
    2. This gives us the third term in our polynomial
    1. The last terms are 2 and -3
    2. This gives us the fourth term in our polynomial
    1. Multiply out each of the terms in the polynomial to simplify
    1. -12x and 4x are like terms, because they both have x raised to the first power
    2. Combining -12x and 4x gives us -8x
    1. First multiply the first terms
    2. Then multiply the outer terms
    3. Then multiply the inner terms
    4. Then multiply the last terms